Greetings! In today's lesson, we'll unravel the concept of polymorphism in C#'s Object-Oriented Programming (OOP). Grasping polymorphism enables us to use a single entity (a method, class, or interface) to represent different types in various scenarios. Let's proceed.

Polymorphism, a pillar of OOP, allows one object to embody multiple forms. Visualize a button in software; depending on its type (for instance, a submit button or a radio button), the action resulting from pressing it varies. This dynamic encapsulates the spirit of polymorphism!

C# supports various types of polymorphism. Run-time polymorphism, also known as dynamic polymorphism, occurs during runtime and leverages method overriding. Let's observe dynamic polymorphism in action within a simple application involving shapes. The base Shape class has an Area method, which calculates the area for shapes. This method is uniquely implemented in the subclasses Rectangle and Circle.

using System;

abstract class Shape
{
    public abstract double Area();
}

class Rectangle : Shape
{
    private double length;
    private double width;

    public Rectangle(double length, double width)
    {
        this.length = length;
        this.width = width;
    }

    public override double Area()
    {
        return length * width;
    }
}

class Circle : Shape
{
    private double radius;

    public Circle(double radius)
    {
        this.radius = radius;
    }

    public override double Area()
    {
        return Math.PI * radius * radius;
    }
}

class Program
{
    static void Main(string[] args)
    {
        Shape rectangle = new Rectangle(2, 3);
        Console.WriteLine(rectangle.Area()); // Prints: 6.0

        Shape circle = new Circle(5);
        Console.WriteLine(circle.Area()); // Prints: 78.53981633974483
    }
}

Here, polymorphism shines as the Area() method takes on multiple forms while using the same Shape abstract class. It behaves differently depending on whether the object is a Rectangle or a Circle.

The other type of polymorphism that C# supports is compile-time polymorphism, also known as static polymorphism, which operates during compile time and involves method overloading. Let's look at the example of static polymorphism:

using System;

class MathOperations
{
    // Overloaded method for rectangle area
    public double Area(double length, double width)
    {
        return length * width;
    }

    // Overloaded method for circle area
    public double Area(double radius)
    {
        return Math.PI * radius * radius;
    }
}

class Program
{
    static void Main(string[] args)
    {
        MathOperations mathOps = new MathOperations();
        Console.WriteLine(mathOps.Area(5, 2)); // Prints: 10
        Console.WriteLine(mathOps.Area(3));    // Prints: 28.27
    }
}

In this example, polymorphism is demonstrated via method overloading. The Area method has multiple forms, accepting different parameter lists to compute the area of either a rectangle or a circle based on the provided arguments. If one argument is provided, the area method for the circle is called; if two arguments are provided, the area method for the rectangle is called.

This is a clear example of static polymorphism, where the correct method is determined at compile time.